A torsional vibration damping arrangement of this kind is known from US published application US-2010-0090382-A1. This known torsional vibration damping arrangement has a primary side and a secondary side which is coupled with the primary side via a damper fluid arrangement for rotation around a rotational axis and for relative rotation with respect to one another. The damper fluid arrangement comprises in a first damper fluid chamber arrangement a first damper fluid with less compressibility which transmits a torque between the primary side and the secondary side and comprises in a second damper fluid chamber arrangement a second damper fluid which has greater compressibility and which is loaded during a pressure increase of the first damper fluid in the first damper fluid chamber arrangement. The second damper fluid chamber arrangement comprises a plurality of preferably substantially cylindrical chamber units which are arranged radially outwardly and/or radially inwardly with respect to the first damper fluid chamber arrangement and successively in circumferential direction. A separating element which separates the first damper fluid from the second damper fluid and which is substantially radially displaceable when there is a change in pressure in the chamber unit is associated with each chamber unit. The advantage of this vibration reducing system consists in that the stiffness can be adjusted substantially as low as required, which enables a very good decoupling of the torsional vibrations of the internal combustion engine. However, the disadvantage is that the torsional vibrations cannot be reduced sufficiently in a simple coupled oscillator in spite of the lowest possible stiffness because, even when reduced to close to zero, a side shaft stiffness in the vehicle associated with the rest of the drivetrain defines the vibrational behavior of the entire drivetrain.
It is thus an object of the present invention to provide a torsional vibration damping arrangement for a drivetrain in a vehicle with which an efficient reduction of torsional vibrations in the torque transmitted in a drivetrain can be achieved in a compact construction and with a low mass moment of inertia.